(Subject to revision according to progress in teaching plan).
L.C. Evans: Partial Differential Equations, 1998. Amer. Math. Soc.. ISBN:?0-8218-0772-2. Graduate Studies in Mathematics, Volume 19.
Material covered in Evans' book :
Sections 3.2 (Characteristics), 3.3.1 and 3.3.2 until theorem 4 (intro to Hamilton-Jacobi), 3.4.1 and 3.4.3, excluding proof of thm 3, and 3.4.4. (intro to Conservation Laws).
Chapter 10 (Hamilton-Jacobi equations): Everything but the proof of the lemma and theorem 1 in section 10.2, and the proof of theorem 3 in section 10.3.4.
Section 2.3: Everything but the proof of theorem 3, subsections 2.3.3 b,c and 2.3.4 b
Section 2.4: Everything but subsections 2.4.1 d,e and 2.4.3 b.
Section 5.5: Definitions and theorems, but no proofs. Section 5.9.1: Everything. Section 5.9.2: Definitions and theorem 3, without proof.
Chapter 7: Everything in sections 7.1.1 and 7.1.2. Section 7.1.4: Theorem 8, with proof.
Chapter 8: Everything in sections 8.1.1, 8.1.2, 8.1.3, 8.2.1, 8.2.2.